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We give a proof of the well-known fact that the $\Ok$-module $\E$ of smoothfunctions is flat by means of residue theory and integral formulas. A variantof the proof gives a related statement for classes of functions of lowerregularity. We also prove a Brian\c{c}on-Skoda type theorem for ideals of theform $\E a$, where $a$ is an ideal in $\Ok$.

The flatness of the $\Ok$-module of smooth functions and integral representation